Chapter 6. On the Parameter Estimation by Method of Moments and Wald Type Test for Poisson Processes

Abstract

We consider two statistical problems for inhomogeneous Poisson processes. The first one concerns the parameter estimation and the second one is about the goodness of fit test. We develop the method of moments in parameter estimation problem and describe the asymptotic behavior of the new test based on the method of moments estimator. We show that the constructed estimators are consistent and asymptotically normal and for the test we find the limit distribution of the test statistics under hypothesis and show its consistency.